Room Modes Calculator

In a rectangular room with rigid walls, standing waves form at frequencies where the room dimensions are integer multiples of half-wavelengths. The resonant frequency for mode $$(n_x, n_y, n_z)$$ is:

$$f = \frac{c}{2}\sqrt{\left(\frac{n_x}{L}\right)^2 + \left(\frac{n_y}{W}\right)^2 + \left(\frac{n_z}{H}\right)^2}$$

where $$c$$ is the speed of sound, $$L$$, $$W$$, $$H$$ are the room dimensions, and $$n_x$$, $$n_y$$, $$n_z$$ are non-negative integers (not all zero).

Modes are classified by how many indices are non-zero:

• Axial modes (1 non-zero index): Strongest, involve two parallel surfaces. Example: (1,0,0) is the first mode between the two walls separated by length L.
• Tangential modes (2 non-zero indices): Involve four surfaces, roughly half the energy of axial modes.
• Oblique modes (3 non-zero indices): Involve all six surfaces, roughly one-quarter the energy of axial modes.

The first axial mode along each dimension is $$f = c/(2d)$$ where $$d$$ is the dimension. For a 5.5 m long room, this is 343/(2 × 5.5) = 31.2 Hz. Evenly distributed modes create smoother bass response; clustered modes create boomy or hollow spots.

Ideally, room modes should be evenly spaced in frequency to avoid peaks and nulls in the bass response. Rooms with dimensions in simple integer ratios (e.g., 1:1:1 or 1:2:3) produce clustered, coincident modes and uneven bass. Recommended ratios include 1:1.28:1.54 (Bolt's ratio) or the golden ratio-based 1:1.618:2.618. Bass traps placed in corners (where all axial modes have maximum pressure) are the most effective treatment for modal problems.